Odrisamer was 3-5 with 10 saves and a 3.78 ERA in 34 games for the 2007-2008Industriales. He tied for 7th in the league in games pitched and tied Vladimir García for 4th in saves. Through that season, his 3rd, he was 12-8 with 18 saves and a 3.68 ERA in 97 games.

Despaigne went 6-6 with a save and a 4.83 ERA in 2008-2009, moving into the rotation for most of the year. He was 10-7 with a 4.30 ERA in 2009-2010 and fanned 106 in 117 1/3 IP. He tied Ciro Licea, Yoelkis Cruz and Ubisney Bermudez for the league lead with 20 games started. Odrisamer tied for 5th in the loop in victories and was second to fellow converted reliever Vladimir García in strikeouts, 9 back of the lead. He was 6th in the league with 55 walks and tied for 4th with 15 hit batsmen.

Despaigne defected from Cuba following the 2012-13 season and signed with the San Diego Padres. He started his professional career in may of 2014 with the San Antonio Missions of the Texas League, where he made two starts, with a 1.17 ERA. He moved up to AAA and the El Paso Chihuahuas and was 1-3, 7.61 in 5 starts before getting the call to San Diego. In his big league debut on June 23rd, he pitched 7 scoreless inning in a 6-0 win over the San Francisco Giants. On July 20th, in just his 5th major league start, Despaigne held the New York Mets hitless through 7 2/3 innings before surrendering a double to 2B Daniel Murphy. Murphy was then driven in by 3B David Wright and Despaigne was subsequently removed from the game, ending up with a no-decision in spite of a brilliant effort. Had he completed the no-hitter, it would have been the first in the history of the Padres. He finished the season with a 4-7 record in 16 starts at the big league level, in spite of a 3.36 ERA and only 85 hits allowed in 96 1/3 innings. He also struck out 65 while walking 32. He showed a very strong home/road split, with a 1.73 ERA at Petco Park and a 1-6, 5.31 mark on the road.

Despaigne was back in the starting rotation for the Padres at the start of 2015 and got off to a strong start, giving up only 3 earned runs in 18 1/3 innings over his first three starts, to start off 2-0, 1.47. He also collected his first major league hit on April 20th, a single off Christian Friedrich of the Colorado Rockies. Things went downhill from there, however, as he won only once more until July 26th. For some reason, the Padres used him in relief for a few games after his strong start. He was hit hard in his first two starts in May, giving up 15 runs in 8 innings. After falling to 5-8, 5.11 after a losing start on August 6th, he was moved to the bullpen for good, making only one more start the rest of the way. He did not pitch in many critical situations and he ERA kept rising. He finished the year at 5-9, 5.80 in 34 games, including 18 starts. He struck out only 69 batters in 125 2/3 innings, or less than 5 per 9 innings. The Padres had clearly given up on him and on February 4, 2016, he was sent to the Baltimore Orioles in return for Class A pitcher Jean Cosme.